SCHEDULE 13G

Amendment No. 7 
Alaska Air Group Incorporated 
common stock 
Cusip # 011659109                

Cusip # 011659109           
Item 1: Reporting Person - FMR Corp.
Item 4: Commonwealth of Massachusetts
Item 5: 105,900 
Item 6: 0 
Item 7: 176,700 
Item 8: 0 
Item 9: 176,700 
Item 11:        0.674% 
Item 12:            HC

Cusip # 011659109    
Item 1: Reporting Person - Edward C. Johnson 3d 
Item 4: United States of America
Item 5: 0 
Item 6: 0 
Item 7: 176,700 
Item 8: 0 
Item 9: 176,700 
Item 11:        0.674% 
Item 12:        IN 

Cusip # 011659109      
Item 1: Reporting Person - Abigail P. Johnson 
Item 4: United States of America
Item 5: None 
Item 6: None 
Item 7: 176,700 
Item 8: None 
Item 9: 176,700 
Item 11:        0.674% 
Item 12:            IN

SCHEDULE 13G - TO BE INCLUDED IN STATEMENTS
FILED PURSUANT TO RULE 13d-1(b) or 13d-2(b)

Item 1(a).      Name of Issuer: 

Alaska Air Group Incorporated 

Item 1(b).      Name of Issuer's Principal Executive Offices:

19300 Pacific Highway South,    
Seattle, WA  98188  

Item 2(a).      Name of Person Filing: 

FMR Corp.

Item 2(b).      Address or Principal Business Office or, if None, 
Residence:

82 Devonshire Street, Boston, Massachusetts  02109

Item 2(c).      Citizenship:

Not applicable

Item 2(d).      Title of Class of Securities:

common stock 

Item 2(e).      CUSIP Number:  

011659109 

Item 3. This statement is filed pursuant to Rule 13d-1(b) or 13d-
2(b) and the person filing, FMR Corp., is a parent holding company in 
accordance with Section 240.13d-1(b)(ii)(G).  (Note:  See Item 7).

Item 4. Ownership

(a)     Amount Beneficially Owned:      176,700 

(b)     Percent of Class:       0.674% 

(c)     Number of shares as to which such person has:  

(i)     sole power to vote or to direct the vote:       105,900 

(ii)    shared power to vote or to direct the vote:     0 

(iii)   sole power to dispose or to direct the disposition of:
176,700 

(iv)    shared power to dispose or to direct the disposition of:
0 

Item 5. Ownership of Five Percent or Less of a CommonStock.

If this statement is being filed to report the fact that as of 
the date hereof, the reporting person has ceased to be the beneficial 
owner of more than five percent of the class of securities, check the 
following (X).

Item 6. Ownership of More than Five Percent on Behalf of Another 
Person.

Not applicable

Item 7. Identification and Classification of the Subsidiary Which 
Acquired the Security Being Reported on By the Parent Holding Company.

See attached Exhibit(s) A, B. 

Item 8. Identification and Classification of Members of the Group.

Not Applicable. See attached Exhibit A. 

Item 9. Notice of Dissolution of Group.

Not applicable.

Item 10.        Certification.

Inasmuch as the reporting persons are no longer the beneficial 
owners of more than five percent of the number of shares outstanding, 
the reporting persons have no further reporting obligation under 
Section 13(d) of the Securities and Exchange Commission thereunder, and 
the reporting persons have no obligation to amend this Statement if any 
material change occurs in the facts set forth herein.

Signature

After reasonable inquiry and to the best of my knowledge and 
belief, I certify that the information set forth in this Schedule 13G 
in connection with FMR Corp.'s beneficial ownership of the common stock 
of Alaska Air Group Incorporated at December 31, 1998 is true, complete 
and correct. 

February 01, 1999 
Date

/s/Eric D. Roiter
Signature

Eric D. Roiter  
Duly authorized under Power of Attorney
dated December 30, 1997, by and on behalf
of FMR Corp. and its direct and indirect
subsidiaries

SCHEDULE 13G - TO BE INCLUDED IN STATEMENTS
FILED PURSUANT TO RULE 13d-1(b) or 13d-2(b)

Pursuant to the instructions in Item 7 of Schedule 13G, Fidelity 
Management & Research Company ("Fidelity"), 82 Devonshire Street, 
Boston, Massachusetts 02109, a wholly-owned subsidiary of FMR Corp. and 
an investment adviser registered under Section 203 of the Investment 
Advisers Act of 1940, is the beneficial owner of 68,600 shares or 
0.261% of the common stock outstanding of Alaska Air Group Incorporated  
("the Company") as a result of acting as investment adviser to various 
investment companies registered under Section 8 of the Investment 
Company Act of 1940.

Edward C. Johnson 3d, FMR Corp., through its control of Fidelity, 
and the funds each has sole power to dispose of the 68,600 shares owned 
by the Funds.

Neither FMR Corp. nor Edward C. Johnson 3d, Chairman of FMR 
Corp., has the sole power to vote or direct the voting of the shares 
owned directly by the Fidelity Funds, which power resides with the 
Funds' Boards of Trustees.  Fidelity carries out the voting of the 
shares under written guidelines established by the Funds' Boards of 
Trustees.

Fidelity Management Trust Company, 82 Devonshire Street, Boston, 
Massachusetts 02109, a wholly-owned subsidiary of FMR Corp. and a bank 
as defined in Section 3(a)(6) of the Securities Exchange Act of 1934, 
is the beneficial owner of  108,100 shares or 0.412% of the common 
stock outstanding of the Company as a result of its serving as 
investment manager of the institutional account(s). 

Edward C. Johnson 3d and FMR Corp., through its control of 
Fidelity Management Trust Company, each has sole dispositive power over 
108,100 shares and sole power to vote or to direct the voting of 
105,900 shares, and no power to vote or to direct the voting of 2,200 
shares of common stock owned by the institutional account(s) as 
reported above.

Members of the Edward C. Johnson 3d family and trusts for their 
benefit are the predominant owners of Class B shares of common stock of 
FMR Corp., representing approximately 49% of the voting power of FMR 
Corp.  Mr. Johnson 3d owns 12.0% and Abigail Johnson owns 24.5% of the 
aggregate outstanding voting stock of FMR Corp.  Mr. Johnson 3d is 
Chairman of FMR Corp. and Abigail P. Johnson is a Director of FMR Corp.  
The Johnson family group and all other Class B shareholders have 
entered into a shareholders' voting agreement under which all Class B 
shares will be voted in accordance with the majority vote of Class B 
shares.  Accordingly, through their ownership of voting common stock 
and the execution of the shareholders' voting agreement, members of the 
Johnson family may be deemed, under the Investment Company Act of 1940, 
to form a controlling group with respect to FMR Corp.

.

SCHEDULE 13G - TO BE INCLUDED IN STATEMENTS
FILED PURSUANT TO RULE 13d-1(b) or 13d-2(b)
RULE 13d-1(f)(1)  AGREEMENT

The undersigned persons, on February 01, 1999, agree and consent 
to the joint filing on their behalf of this Schedule 13G in connection 
with their beneficial ownership of the common stock of Alaska Air Group 
Incorporated at December 31, 1998.

FMR Corp.

By   /s/Eric D. Roiter                          
Eric D. Roiter
Duly authorized under Power of Attorney
dated December 30, 1997, by and on behalf
of FMR Corp. and its direct and indirect 
subsidiaries

Edward C. Johnson 3d

By   /s/Eric D. Roiter                          
Eric D. Roiter
Duly authorized under Power of Attorney
dated December 30, 1997, by and on behalf
of Edward C. Johnson 3d

Abigail P. Johnson

By   /s/Eric D. Roiter                          
Eric D. Roiter
Duly authorized under Power of Attorney
dated December 30, 1997, by and on behalf
of Abigail P. Johnson

Fidelity Management & Research Company

By   /s/Eric D. Roiter                          
Eric D. Roiter
V.P. and General Counsel